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Homework Help: Beer'Lamberts Law

  1. Mar 8, 2010 #1
    1. The problem statement, all variables and given/known data

    I am trying to understand a formula on a paper. On page 3138-3139 they express the Beer-Lamberts law in which they replace the concentration n with an equation involving the volume ratio ( I am guessing its the molarfraction of the investigated species). What I would like to know is the unit of Boltzmann constant kb to make this happen. I don't see how the units can fit.

    2. Relevant equations


    where c is the volume part (volume ratio) of the absorbing gas in the gas mixture, T is the temperature of the gas, k is the boltzmann constant (unit???), p is pressure in [atm].

    3. The attempt at a solution

    This equation should fit to Beer law,

    exp( - alpha(v)*n*l ) = exp (- tau )

    where tau is unitless and alpha(v) is specific absorption coefficient per
    absorbing particle and is caluclated with help of Hitran by alpha(v) = S(T)*g(v-vo) [ unit: 1/(molecule cm-2) ] and l is path length of radiation through the absorbing medium [ unit: cm ].

    It's the unit of n I am trying to determine, and thus boltzmann constant.

    According to above it should be [molecules cm-3] so that tau becomes unitless.

    What I know the unit if Kb is 0.659 cm-1 K-1. And there is the [ atm ] from the pressure I am missing and [ molecules ]. If c is a fraction this is unitless, so I don't see how this can go together.

    This has been taken from this paper: http://iopscience.iop.org.ludwig.lub.lu.se/0022-3727/35/23/315/pdf/0022-3727_35_23_315.pdf

    "Experimental verification of gas spectra calculated for high temperatures using the
    HITRAN/HITEMP database"

    My goal is to plot the transmission as function of % of the species.
    Last edited: Mar 8, 2010
  2. jcsd
  3. Mar 8, 2010 #2


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    Staff: Mentor

    You are aware of the fact that paper you linked to is available only to those that can log in?
  4. Mar 8, 2010 #3
    Well, yes. That is why I have written everything in detail. However if you have access to the university as student or teacher you should be able to log in and read it.

    I noticed that the unit is [ cm -2 atm -1 ] for the linestrength S. In hitran this is [ cm-1 / ( molecules cm-2 ) ] and absorption coefficent is [ cm-1].

    I don't see the connection.
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